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A Novel Aerodynamic Design Method for Centrifugal
Compressor Impeller
M. Nili-Ahmadabadi1, M. Durali
2 and A. Hajilouy
2
1 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran 2 School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
†Corresponding Author Email: m.nili@cc.iut.ac.ir
(Received April 3, 2013; accepted May 9, 2013)
ABSTRACT
This paper describes a new quasi-3D design method for centrifugal compressor impeller. The method links up a
novel inverse design algorithm, called Ball-Spine Algorithm (BSA), and a quasi-3D analysis. Euler equation is
solved on the impeller meridional plane. The unknown boundaries (hub and shroud) of numerical domain are
iteratively modified by BSA until a target pressure distribution in flow passage is reached. To validate the quasi-
3D analysis code, existing compressor impeller is investigated experimentally. Comparison between the quasi-3D
analysis and the experimental results shows good agreement. Also, a full 3D Navier-Stokes code is used to
analyze the existing and designed compressor numerically. The results show that the momentum decrease near the
shroud wall in the existing compressor is removed by hub-shroud modifications resulting an improvement in
performance by 0.6 percent.
Keywords: Centrifugal compressor, Inverse design, Quasi-3D, CFD, Ball spine Algorithm (BSA).
NOMENCLATURE
a linear acceleration (m.s-2) y y position of joints (m), y coordinate
A local area of duct wall (m2) W relative velocity (m/s)
BSA ball spine algorithm Δ difference
CPD current pressure distribution on the wall Δt time step(s)
CPrD current reduced pressure distribution ΔPi difference between tpd and cpd at each link
F force vector (N) θ angle between spine and force direction (deg)
FSA flexible string algorithm ρ density of fluid (kg.m-3), surface density (kg.m-2)
m ball mass (kg) ηtt total to total efficiency
n number of virtual balls, normal to wall ω angular velocity (rad.s-1)
P static pressure (Pa) Subscripts P0 stagnation pressure (Pa) dp Design point (maximum efficiency)
P0r relative stagnation pressure (Pa) i Balls index
Pr reduced pressure (Pa) S Spine direction
r radial coordinate, radius (m) Superscripts SSD surface shape design I.G. initial guess
Journal of Applied Fluid Mechanics, Vol. 7, No. 2, pp. 329-344, 2014.
Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.
DOI: 10.36884/jafm.7.02.20279
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
330
t tangent to wall out impeller outlet
TPD target pressure distribution t+Δ t related to updated geometry
TPrD target reduced pressure distribution t related to current geometry
x x position of joints (m), x coordinate
1. INTRODUCTION
Design of gas turbine components such as intakes,
manifolds, duct reducers, and compressor and turbine
blades involves shape determination of solid elements
while fluid flow or heat transfer rate is optimal in
some sense. The technological limitations and
computational costs are challenging obstacles in such
problems.
One of the known optimal shape design methods is
Surface Shape Design (SSD). SSD in fluid flow
problems involves finding a shape associated with a
prescribed distribution of surface pressure or velocity.
It should be mentioned that the solution of a SSD
problem is not necessarily an optimum solution in
mathematical sense. It just means that the solution
satisfies a Target Pressure Distribution (TPD) which
resembles a nearly optimum performance (Ghadak
2005).
There are basically two different algorithms for
solving SSD problems namely decoupled (iterative)
and coupled (direct or non-iterative). In the coupled
solution approach, an alternative formulation of the
problem is used in which the surface coordinates
appear (explicitly or implicitly) as dependent
variables. In other words, the coupled methods tend to
find the boundary and flow field unknowns
simultaneously in a (theoretically) single-pass or one-
shot approach (Ghadak 2005).
The iterative shape design approach relies on repeated
shape modifications such that each iteration consists
of flow solution followed by a geometrical updating
scheme. In other words, a series of sequential
problems are solved in which the surface shape is
changed between iterations till desired TPD is
achieved (Ghadak 2005).
Iterative methods, such as optimization techniques,
are widely used in solving practical SSD problems.
The traditional iterative methods used for SSD
problems are often based on trial and error
algorithms. This trial and error process is very time-
consuming and computationally expensive. Hence it
relies on designer experience for reducing the costs.
Optimization methods (Cheng et al. 2000 and
Jameson 1994) are used to automate the geometry
modification in each iteration cycle. In such methods,
an objective function (e.g., the difference between a
current surface pressure and a target surface pressure
(Kim et al. 2000)), subject to flow constraints is
minimized. Although the iterative methods are
general and powerful, they are often time consuming
and mathematically complex.
Other iterative methods presented so far, use the
physical algorithms instead of the mathematical
algorithms to automate the geometry modification in
each iteration cycle. These methods are relatively
easier and quicker. One of these physical algorithms is
governed by a transpiration model in which one can
assume the passage wall is porous. This implies that
mass is fictitiously injected through the wall in such a
way that the new wall satisfies the slip boundary
condition. Aiming the elimination of nonzero normal
velocity at the boundaries, a geometry update must be
adopted. This update is determined by applying either
the transpiration model based on mass flux
conservation (Dedoussis et al. 1993, Demeulenaere et
al. 1998, De Vito et al. 2003, Leonard et al. 1997 and
Henne 1980), or streamline model based on alignment
with the streamlines (Volpe 1989).
An alternative algorithm is based on the residual-
correction approach. In this method, the key problem
is to relate the calculated differences between the
actual pressure distribution on the estimated geometry
and the TPD )the residual (to the required changes in
the geometry .ybviously ,the art in developing a
residual-correction method is to find an optimum state
between the computational effort )for determining the
required geometry correction (and the number of
iterations needed to obtain a converged solution .This
geometry correction may be estimated by means of a
simple correction rule ,making use of relations
between geometry changes and pressure differences
known from linearized flow theory (Ghadak 2005).
The residual-correction decoupled solution methods
try to utilize the analysis methods as a black-box .
Barger et al. (1974) presented a streamline curvature
method in which they considered the possibility of
relating a local change in surface curvature to a change
in local velocity .Since then , a large number of
methods have been developed on the basis of that
concept (Garabedian et al. 1982, Malone et al. 1986,
1985, Campbell et al. 1987, Bell et al. 1991, Malone
et al. 1989, 1991, Takanashi et al. 1985, Hirose et al.
1987, Dulikravich et al. 1999 (.
The role of quasi-3D flow analysis relative to the
detailed aerodynamic design of impellers is described
in Aungier (2000). The key feature that keeps the
quasi-3D Euler codes firmly entrenched over available
exact viscous CFD codes in almost all design systems
is the computational speed. The procedure of quasi-3D
flow analysis can generate a solution in a matter of
seconds even on a personal computer of modest
capability. Currently, this seems the only analysis
method that a designer needs for an efficient, fast and
detailed component design.
For centrifugal compressor impeller, comparison
between quasi-3D flow analysis and experimental
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
331
results shows good agreement, except near trailing
and leading edges, where the experimental data shows
higher velocities than those predicted by the analysis
(Aungier 2000).
Vanco (1972) gives the results of quasi-3D flow
analysis used to find the flow distribution in the
meridional plane of a centrifugal compressor. This
method solves the velocity gradient equations with
the assumption of a hub-to-shroud mean stream
surface. A set of fixed arbitrary straight lines from
hub to shroud is used instead of normal lines called
quasi-orthogonal lines. These lines are independent of
streamline changes. The work then determines the
velocities in the meridional plane of a back-swept
impeller, a radial impeller, and a vaned diffuser, as
well as approximate blade surface velocities.
Zangeneh et al. (1988) found the presence of a high
loss region in the passage and pointed out that the
high loss region is similar to the "jet/wake"
phenomenon observed in centrifugal compressors.
They indicated that the high loss region is generated
by the secondary flows. This secondary flow moves
the low momentum fluids under the action of reduced
static pressure towards the corner of shroud-suction
side near the trailing edge.
Recently, Nili et al. (2009, 2009 and 2008) have
presented a novel inverse design method called
Flexible String Algorithm (FSA). They developed
this method for non-viscous compressible and viscous
incompressible internal flow regime, but FSA was not
capable of axisymmetric and 3D design cases.
In the current research, using the physical bases of
FSA, a novel inverse design algorithm called Ball-
Spine Algorithm (BSA), simpler to the FSA, is
presented for duct design. In BSA compared to FSA,
the unknown walls are composed of a set of virtual
balls, instead of flexible string, that move freely along
specified directions called spines. The difference
between the target and current pressure distribution
on walls, move the balls along the spines.
Considering that the BSA is an iterative inverse
design method, it should be incorporated into a flow
analysis code. In this investigation, a quasi-3D code
solving Euler equation on the meridional plane of a
centrifugal compressor is combined with BSA. The
computational tool is employed in decreasing the high
loss region near the shroud wall by modifying the
pressure distribution along the hub and shroud wall.
The walls are changed during the process to satisfy
the modified pressure distributions. Full 3-D Navier-
Stokes solutions of the original and the modified
compressors were then compared. To validate the
solutions from fully 3D Navier-Stokes and quasi-3D
codes, experimental investigation was performed at
Sharif Gas Turbine Lab.
2. FUNDAMENTALS OF METHOD
A 2-D flexible duct whose walls are composed of a
set of virtual balls, freely moving along a specified
direction, is shown in Fig. 1. Passing fluid through the
flexible duct causes a pressure distribution to be
applied to the inner side of duct wall. If a target
pressure distribution is applied to the outer side of
each duct wall, the flexible wall deforms to reach to a
shape satisfying the target pressure distribution on the
inner side. In other words, the force due to the
difference between the target and current pressure
distribution at each point of the wall is applied to each
virtual ball and force them to move. As the target
shape is reached, this pressure difference logically
vanishes. If a virtual ball moves in the applied force
direction, the adjacent balls may collide together or
move away from each other. This can disturb the wall
modification procedure. To avoid this problem, the
balls should freely move in specified directions called
spine. In Fig. 1, the spines are the normal line
connecting the balls with the same x position on the
two walls. In other words, the horizontal length of the
duct remains unchanged during the shape modification
procedure. In duct inverse design problems, it is
essential that a characteristic length remains fixed. The
direction of spines depends on the fixed length.
Therefore, for different ducts, the spines are
differently defined. Another constraint on this wall
modification process is keeping one fixed point on
each wall. Typically, the starting point of each wall is
fixed so that the duct inlet area remains fixed too.
Fig. 1. Simulation of a 2-D duct with balls and spines.
2.1 Governing Equations
To derive kinematic relations of the flexible wall, a
uniform mass distribution along the wall is assumed.
Free body diagram of a virtual ball is shown in Fig. 2.
Fig. 2. Free body diagram of a ball.
The basic equations relations can be derived as
follows:
m
APamaAPF SSS
cos cos
(1)
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
332
2
2
1tay S
(2)
If (ρ) is defined as wall surface density, the following
relation can be written:
cos
2
cos
2
12
2P
tt
A
APy
(3)
(∆t) is an interval for ball movement at each shape
modification step. The parameter (∆t2/ρ) is an
adjusting parameter for the convergence rate of BSA
method. The lower the value of (∆t2/ρ), the slower the
convergence rate will be. Indeed, if (∆t2/ρ) exceeds a
limit, the design algorithm will diverge. The new
position of each ball for a horizontal duct as shown in
Fig. 1 is obtained from the following relations:
(4) t
i
tt
i xx
(5) ii
t
i
tt
i Pt
yy
cos2
2
In the meridional plane of a centrifugal compressor,
the outlet radius instead of horizontal length should
be fixed. In such geometry, the arbitrary straight lines
from hub to shroud are the best choice for the spines.
In Fig. 3, the schematic of ball displacement along the
spine for the meridional plane is shown.
Fig. 3. Schematic of ball displacement along spine
Similar to other iterative inverse design methods, the
flow field should be analyzed at each shape
modification step. In this paper, the numerical
techniques presented in (Zangeneh et al. 1988) are
used for quasi-3D flow analysis. The spines used for
inverse design are the same quasi-orthogonal lines used for quasi-3D analysis.
2.2 Applying Pressure Difference to Each
Virtual Ball
As known, in inviscid flow, the stagnation pressure
and relative stagnation pressure are constant along
each stream line for stationary and rotating ducts,
respectively.
(6) 2
02
1VPP
(7) 222
02
1
2
1 rWPP r
Defining reduced pressure as follows:
(8) 22
2
1rPPr
relative stagnation pressure can be rewritten as:
(9) 2
02
1WPP rr
Analogy between Eq. (6) and (9) shows that the
stagnation pressure, static pressure and velocity are
replaced by the relative stagnation pressure, reduced
pressure and relative velocity, respectively. In other
words, reduced pressure is sensed from rotating duct
wall similar to static pressure being sensed from
stationary duct wall. Therefore, the growth of
boundary layer thickness along the rotating duct wall
depends on the reduced pressure gradient. Also, for
inverse design of a rotating ducts such as centrifugal
compressor meridional plane, the difference between
the current and target reduced pressures is applied to
each virtual ball on the wall. Finally, the displacement
of each ball along its spine is obtained from the
following equation:
(10)
)()(cos2
arg
2
iPiPt
s rettrii
Because the starting point of each wall should be fixed
during the design procedure, the inlet reduced pressure
is considered as inlet boundary condition for quasi-3D
analysis code and remains fixed for the first virtual
ball on the wall.
3. BSA DESIGN PROCEDURE
Figure 4 shows how BSA is typically combined with
existing flow solution procedures. The computed
pressure surfaces are normally obtained from partially
converged numerical solutions of the flow equations.
During the iterative design procedure, as the CPrD
approaches to the TPrD, the force applied to the
flexible wall gradually vanishes. At final steps, the
subsequent solutions of the flexible wall equations yield no changes in the duct surface coordinates.
3.1 Quasi-3D Analysis
To perform a quasi-3D analysis of a centrifugal
compressor at its meridional plane, it is necessary to
specify the input parameter. These quantities consist of
mass flow rate, rotational speed, number of blades,
specific-heat ratio, inlet total temperature and density,
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
333
gas constant, hub-to-shroud profile, mean blade
shape, and a normal thickness distribution of blades.
Mass flow rate, rotational speed, inlet total
temperature and density are obtained from
experimental measurements at the compressor inlet at
design point. The numerical values of the input
parameters are specified in Table 1.
To determine the mean blade shape of the radial
impeller, the angular coordinate of the mean blade
shape is specified as a function of the axial distance,
as shown in Fig. 5. Solution is started by an initial
guess for streamlines. After the solution convergence,
the streamlines are obtained as shown in Fig. 6.
Figure 7 shows the reduced pressure distribution
along the hub and shroud. Keen adverse gradient of
the reduced pressure on the shroud causes the
boundary layer thickness to grow.
In Fig. 8, the contour of static pressure is shown. As
expected, the static pressure increases through the
impeller. The contour of reduced pressure is shown in
Fig. 9. Figure 10 shows the relative velocity contour.
As can be seen in this figure, the maximum relative
velocity occurs near the shroud at the inlet.
Table1 Centrifugal compressor parameters
Parameter(unit) Value
Operational condition Design point
Number of impeller
blades
25
Specific-heat ratio 1.4
Gas constant (J/(kg.K)) 287
Inlet flow angle (°) 0.0
Inlet total temperature
(K°)
322
Inlet total density
(kg/m3)
1.088
Fig. 4. Implementation of the inverse design algorithm
Fig. 5. Mean blade shape for radial impeller Fig. 6. Hub-to-shroud profile of radial impeller with its
streamlines
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 0.2 0.4 0.6 0.8 1
Dimensionless Length
Teth
a (
rad
)
Compute the Difference
between
TPrD and CPrD
Updating
Geometry TPrD
Initial Guess
for Unknown
Duct Walls
Computational
Grid
Generation
Quasi-3D
Analysis of the
Meridional Plane Start
Converged? Stop BSA Design
Procedure
No Yes
Flow Analysis Procedure
Compute the
Flexible Wall
Displacement
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
334
Fig. 7. Reduced pressure distribution along hub and
shroud
Fig. 8. Contour of static pressure on the meridional
plane
Fig. 9. Contour of reduced pressure on the meridional
plane
Fig. 10. Contour of relative velocity on the meridional
plane
3.2 Inverse Design Validation Test Case
For validation of the proposed method, the reduced
pressure distributions along the hub and shroud in
Fig. 7 are considered as our TPrD for the SSD
problems. The method should converge from an
initial arbitrary shape to the shape shown in Fig. 6.
Initiating from a meridional plane with larger area
ratio, the design program algorithm is converged after
450 modification steps. Figure 11 shows the
modification procedure from the initial guess to the
target shape. The iterations are stopped after the
design residual defined by the following equation
reaches 10-3.
(11)
N
iietT
N
iietTi
P
PP
residual
1
arg
1
arg
Fig. 11. Wall shape modification procedure
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335
After each geometry modification step, the quasi-3D
analysis code is run until the residuals of the analysis
code are reduced by 3 orders of magnitude. The
residual of the analysis code is defined as the change
in conserved flow variables (∑│(Qn+1-Qn)/QI.G.│) and
is normalized by the residual of the first iteration.
These convergence criteria for the design algorithm
and analysis code are enough to confirm the required
convergence so that the difference between calculated
and target shapes cannot be recognized. Additional
reduction of the residuals will just increase the
computational time.
4. 3-D NUMERICAL SIMULATION
OF COMPRESSOR
Hub and shroud profile modification is the final target
of this process. The quasi-3D analysis code, which is
incorporated into the inverse design algorithm, is
based on inviscid flow and cannot estimate the
performance. A fully 3D viscous code is used to
analyze the flow field of the compressor for
evaluation of the quasi-3D analysis results. Also, it
can be used for performance prediction of the current
and modified compressor.
4.1 Numerical Method and Boundary
Conditions
The centrifugal compressor is composed of a radial
impeller with 25 blades and a radial vaned diffuser
with 24 blades. The first and most important step of
the numerical simulation of flow inside the
compressor is the geometry definition and grid
generation. This step is usually the most time-
consuming part. Selection of grid type and locations
for grid refinements are the next important tasks. In
this simulation, structural elements are used for grid
generation of impeller and diffuser. Finer grids are
used for zones having steep gradients such as points
adjacent to the walls and blades.
The Reynolds-Averaged Navier-Stokes equations
(RANS) which describe the conservation of mass,
momentum and energy, are solved by means of a
finite volume method. Discretization of the equations
is done via a coupled implicit method in which the
energy, momentum and mass equations are solved
simultaneously. The Reynolds stress terms in the
momentum transport equations are resolved using the
shear-stress transport (SST) turbulence model. This
turbulence model is developed to blend the robust and
accurate formulation of the k-ω model in the near-
wall region with the free-stream independence of the
k-ε model in the far field (Menter et al. 2003).
Using the mixing plane interface model,
computational domain is divided into stationary and
moving zones. This utilizes relative motion between
the various zones to exchange calculated values
between zones. To complete the model in rotating
zones, the coriolis and centrifugal accelerations are
added to the momentum equations. The mixing plane
method is a "non-physical snapshot approach" which
cannot be compared to a snapshot of a transient
simulation. This is because the solution does not know
anything about what happened before, but it mixes the
impeller flow state into the diffuser. The mixing plane
model on the other hand has the advantage that only
one pitch of the impeller and diffuser has to be
modeled. Figure 12 shows one pitch of the impeller
and diffuser with their grids.
Fig. 12. Compressor Geometry with its grid
The boundary conditions for this simulation include
mass flow rate and total temperature at the inlet,
average static pressure at the outlet, no slip condition
for stationary walls, zero relative velocity with respect
to the rotating zone for rotating walls, mixing plane for
interface between the impeller, diffuser and periodic
boundary condition. It is noticeable that the quantities
of the boundary conditions are set from experimental
measurements at the inlet and outlet of the compressor
while the compressor works as a part of the gas turbine
along its operation line.
Theoretically, the errors in the solution related to the
grid must disappear by increasing mesh resolution
(Ferziger et al. 1996). The compressor pressure ratio
and efficiency at nominal flow conditions are taken as
the parameters to evaluate three grid configurations
(Fig. 13), and to determine the influence of mesh size
on the solution. The selected convergence criterion
was the attainment to a constant value for drag, lift and
moment coefficients of walls. In Fig. 13, it is observed
how the calculated compressor pressure ratio and
efficiency reach an asymptotic value as the number of
elements increases. According to this figure, the grid B
(648538 elements) was considered to be sufficiently
fine to ensure mesh independency. The y+ value
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
336
changes from 30 to 130 for grid B.
Fig. 13. Effect of grid size on pressure ratio and
efficiency of the compressor
4.2 Current Compressor Flow Field
The 3D numerical analysis is accomplished in
different rotational speeds. In this section, the flow
field contours are shown in maximum efficiency.
Figures 14, 15 and 16 respectively show the static
pressure, absolute Mach number and stagnation
pressure field at half spanwise section between the hub
and shroud in design conditions. As can be seen in
Fig. 14, the static pressure rises from the impeller inlet
toward the diffuser outlet. This is due to increase in
section area inside the impeller and diffuser passage
and, increase in centrifugal force through the impeller.
Figure 15 shows that Mach number at the impeller
outlet and diffuser inlet is near 1 and thus, any
increase in rotational speed can choke the compressor.
In Fig. 16, it is clear that the stagnation pressure
increases through the impeller because of work done
by the impeller on the fluid. In the diffuser, a slight
decrease in stagnation pressure is observed because of
friction loss. Moreover, the stagnation pressure
decreases behind the diffuser blades due to their wake
region.
Figures 17, 18 and 19 show the contours of static
pressure, reduced pressure and relative velocity field
on the periodic section of impeller in design
conditions. These three figures can be compared with
Figs. 8, 9 and 10. In Fig. 19, decrease in relative
velocity near the shroud is related to the growth of
boundary layer thickness due to steep adverse gradient
of reduced pressure. It shows that the pressure
distribution along the shroud needs to be modified to
improve the flow loss.
Other contours of current compressor in comparison
with the modified compressor contours will be
presented in section 6.
Fig. 14. Static pressure contour on the spanwise section Fig. 15. Mach number contour on the spanwise section
1.985
1.987
1.989
1.991
2 4 6 8 10 12 14 16
Number of elements*1e5
To
tal
pre
ssu
re r
ati
o
Grid A
284914 Grid B
648538Grid c
1477128
86.1
86.15
86.2
2 4 6 8 10 12 14 16
Number of elements*1e5
Eff
icie
ncy
Grid A
284914
Grid B
648538 Grid c
1477128
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
337
Fig. 16. Stagnation pressure contour on the spanwise
section
Fig. 17. Static pressure contour on the periodic section
Fig. 18. Reduced pressure contour on the periodic section Fig. 19. Relative velocity contour on the periodic section
4.3 Validation of Quasi-3D Analysis with 3D
Numerical Simulation
Before combining the quasi-3D code with BSA
design algorithm, it is necessary to validate the quasi-
3D analysis results with 3D numerical simulation.
In Fig. 20, the hub pressure distribution resulted from
quasi-3D analysis is compared with results of 3D
numerical simulation. Although viscous and 3D
effects and clearance are ignored in quasi-3D
analysis, it well agrees with 3D simulation. In Fig. 21,
the pressure distribution on the shroud calculated by
quasi-3D, 3D numerical simulation and experimental
measurements are compared. Except next to the inlet
and outlet, a good agreement is observed through the
passage. The deviation in the inlet area is due to flow
deflection at the blade leading edge. The 3D
numerical simulation shows that a momentum
decrease due to flow losses exists at the end of the
shroud wall. Because the losses due to viscous and
3D flow field inside the impeller are not considered in
the quasi-3D analysis, this deviation at the end of the
shroud can be justified. Also, in order to validate the
numerical results, the static pressure is measured at
four points on the shroud at Sharif Gas Turbine Lab.
The numerical results show good agreement with
experimental measurements.
In Fig. 22, a comparison between the quasi-3D and 3D
analysis results is accomplished for the reduced
pressure on the hub and shroud. Similar to the
previous figures, good agreement exists except beside
the inlet and outlet. It shows that the modification of
meridional plane by combining BSA and quasi-3D
code will improve the impeller performance although
the viscous and 3D effects are ignored in the design
process.
5. COMPRESSOR
EXPERIMENTAL SETUP
In this research, the centrifugal compressor is tested as
a component in a gas turbine. The necessary
instruments to measure mass flow and pressures in
different parts of the compressor are added to the gas
turbine test setup. The schematic of experimental
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
338
arrangement is shown in Fig. 23.
The measurements are done at four areas namely;
impeller inlet, shroud wall, impeller outlet and
diffuser outlet. The rotational speed is measured by a
magnetic pick-up and mass flow rate by pressure
difference across the belmouth at the gas turbine inlet.
A total of 11 static pressure taps, 6 stagnation
pressure probes and 8 thermocouples are used for
measuring thermodynamic parameters at different
positions. The variation of total to total isentropic
efficiency and total pressure ratio versus the
normalized rotational speed are extracted from the
experiments.
The experimental performance results are used for
validation of 3D numerical simulation results. In Figs.
24 and 25 the numerical performance is compared
with the experimental performance and shows good
agreement.
Fig. 20. Pressure distribution on the hub due to the quasi 3D
and 3D analysis
Fig. 21. Pressure distribution on the shroud due to the quasi
3D, 3D analysis and experiment
Fig. 22. Reduced pressure distribution on the hub and
shroud due to the quasi 3D and 3D analysis
Fig. 23. Schematic of experimental setup for the centrifugal
compressor of the gas turbine
Fig. 24. Numerical and experimental efficiency Fig. 25. Numerical and experimental total pressure ratio
80000
90000
100000
110000
120000
130000
140000
0 0.2 0.4 0.6 0.8 1
Dimensionless Length
Pre
ss
ure
(p
a)
Hub Pressure_3D-CFD
Hub Pressure_Quasi 3D
80000
90000
100000
110000
120000
130000
140000
0 0.2 0.4 0.6 0.8 1
Dimensionless Length
Pre
ss
ure
(p
a)
Shroud_CFD 3D
Shroud_Quasi 3D
Shroud_Experiment
60000
70000
80000
90000
0 0.2 0.4 0.6 0.8 1
Dimensionless Length
P-r
ed
uc
tio
n (
pa
)
Hub_3D_CFD
Shroud_3D_CFD
Hub_Quasi 3D
Shroud_Quasi 3D
0.75
0.8
0.85
0.9
0.95
1
0.6 0.7 0.8 0.9 1 1.1 1.2
Numrical E ffic iency
E xperimental E ffic iency
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
0.6 0.7 0.8 0.9 1 1.1 1.2
To
tal P
ressu
re R
ati
o
Exprimental
Numerical
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
339
6. DESIGN EXAMPLES
After validating the quasi-3D analysis results, the
BSA design algorithm is incorporated into the quasi-
3D code and the hub-shroud profile of the impeller is
obtained by modifying the reduced pressure
distribution along the hub and shroud.
In Fig. 26, having modified the CPrD, the
corresponding shape of the hub and shroud is
obtained. In this design (design A), the additional
adverse pressure gradient along the shroud is
removed but, the inlet and outlet pressures are not
changed. In other words, keeping the area ratio fixed,
it is tried to make it smooth. Moreover, as seen in Fig.
26, the axial length of the modified impeller is
reduced by 5%.
In design B shown in Fig. 27, a slight increase in
outlet pressure is seen that causes the area ratio to be
increased. Also, the adverse pressure gradient along
the shroud is lower than that of design A. This will
reduce the boundary layer thickening on the shroud. It
is clear that the deflection angle from the inlet to the
outlet depends on the surrounded area between the
reduced pressure distributions along the hub and
shroud. As seen in Fig. 27, this surrounded area for
the modified pressure has been increased compared to
the original case.
In design C (Fig. 28), it is tried to reach to a minimum
adverse pressure gradient on the shroud in such a way
that the inlet and outlet pressure and, the surrounded
area between the hub and shroud pressure remain
unchanged, hence the deflection is unchanged. In this
case, the axial length of the modified impeller is
reduced by 10%. The modifications in design C will
decrease the boundary layer losses, and also the blade
effective area (meridional plane area) and average
pressure level of the blade. Hence, it causes the blade
work to be transferred to the fluid in a lower pressure
level and on a smaller area. Therefore, it is expected
that the pressure ratio of the impeller in design C
decreases.
In cases A, B and C, the impeller hub and shroud were
modified resulting a change in the axial length of the
impeller. It is clear the separation along the shroud is
more probable than along the hub, therefore, to
improve the meridional plane geometry with a
minimum change in geometry and without change in
the axial length, the hub geometry is kept fixed and the
shroud is to be modified. As a result, the reduced
pressure distribution along the hub is out of control
and is obtained automatically.
To specify the TPrD along the shroud, two important
points should be considered. First, the pressure applied
to the fluid in rotating zone is the reduced pressure.
Just as the fluid exits from a rotating zone, the
pressure applied to the fluid changes from the reduced
pressure to the static pressure. In other words, the fluid
is confronted with a pressure jump of 1/2ρr2ω2 that
causes the wake region at the impeller outlet to be
intensified. To overcome this pressure jump, it is
necessary that the fluid be accelerated before exiting
the impeller. The slope of the reduced pressure
distribution on the hub is negative and the fluid is
accelerated before exiting the impeller. The main
problem is related to the shroud along which the
reduced pressure increases. The current distribution of
the reduced pressure along the shroud has an
advantage that the reduced pressure slope at the
impeller outlet is negative and the fluid is accelerated
before exiting. As seen in the TPrD of the design D
(Fig. 29), the reduced pressure along the shroud
increases and suddenly decreases near the end part.
The second point is that in most efficient diffusers, the
passage experiences a high pressure loading at the first
part followed by a moderate one toward its end. As
seen in the TPrD of design D (Fig. 29), this physical
base is followed.
Fig. 26. Design A
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
340
Fig. 27. Design B
Fig. 28. Design C
Fig. 29. Design D
The 3D numerical simulation of design D shows that
the efficiency is improved by 0.6 percent compared to
the original design. The increment of the efficiency
versus the normalized rotational speeds is shown in
Fig. 30. It is noticeable that, there is no difference
between the grid generation of the modified impeller
and that of the current impeller in the 3D numerical
simulation. In Figs. 31-35, the flow field contours of
the modified geometry (design D) are compared with
that of the current geometry. Figure 31 shows that the
relative velocity decrement at the end part of the
shroud is improved for design D. Figure 32 shows the
relative stagnation pressure contour on the periodic
surface of the impeller, indicating the energy losses.
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
341
As seen, the relative stagnation pressure loss near the
shroud is improved. In Fig. 33, the relative stagnation
pressure contour is shown at the impeller outlet for
the current impeller and design D. It shows that the
energy losses near the shroud have been decreased.
The relative velocity contour at the impeller outlet is
shown in Fig. 34. The wake region in the shroud area
is weakened for design. Also, the wake behind the
blade is clearly seen in this figure. The radial velocity
contour at the impeller outlet is shown in Fig. 35,
indicating the removal of small reverse flow region
with negative radial velocity in design D compared to
the original design. Fig. 30. Efficiency improvement versus the rotational
speed
a) Current Impeller b) Design F
Fig. 31. Relative velocity contour on the periodic surface of the impeller
a) Current Impeller b) Design F
Fig. 32. Relative stagnation pressure contour on the periodic surface of the impeller
0.75
0.78
0.81
0.84
0.87
0.9
0.6 0.7 0.8 0.9 1 1.1 1.2
Current Impeller
Design F
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
342
a) Current Impeller b) Design F
Fig. 33. Relative stagnation pressure contour on the impeller outlet
a) Current Impeller b) Design F
Fig. 34. Relative velocity contour on the impeller outlet
a) Current Impeller b) Design F
Fig. 35. Radial velocity contour on the impeller outlet
7. CONCLUSIONS
The BSA turns the inverse design problem into a
fluid-solid interaction scheme that is a physical base
analysis. The BSA is a quick converging method and
can efficiently utilize commercial flow analysis
software as a black-box. In this research, the BSA
design procedure was combined with a quasi-3D
analysis code for designing the hub and shroud
profiles of a centrifugal compressor impeller. For the
convergence of the BSA in a rotating zone, the
difference between the CPrD and TPrD should be
applied to the flexible wall at each shape modification
step. Considering a TPrD on the shroud featuring a
passage high loading at the first part followed by a
moderate one at the middle part and terminated to a
negative one at the end, the design procedure
converges to a shroud profile that improved the
compressor efficiency by 0.6 percent.
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
343
REFRENCES
Ghadak, F. (2005). A ِِDirect Design Method Based on
the Laplace and Euler Equations, Ph. D. Thesis,
Sharif University of Technology, Tehran, Iran.
Cheng, C. H. and C. Y. Wu (2000). An approach
combining body fitted grid generation and
conjugate gradient method for shape design in
heat conduction problems. Numerical Heat
Transfer Part B 37(1), 69-83.
Jameson, A. (1994). Optimal design via boundary
control. Optimal Design Methods for
Aeronautics, AGARD, 3.1 - 3.33.
Kim, J. S. and W. G. Park (2000). Optimized inverse
design method for pump impeller. Mechanics
Research Communications 27(4), 465-473.
Dedoussis, V., P. Chaviaropoulos and K. D. Papailiou
(1993). Rotational compressible inverse design
method for two-dimensional internal flow
configurations. AIAA Journal 31(3), 551-558.
Demeulenaere A. and R. V. D. Braembussche (1998).
Three–dimensional inverse method for
turbomachinary blading design. ASME Journal
of Turbomachinary 120(2), 247–255.
De Vito, L. and R.V.D. Braembuussche (2003). A
novel two-dimentional viscous inverse design
method for turbomachinery blading.
Transactions of the ASME 125, 310-316.
Leonard, O. and R.V.D. Braembuussche (1997). A
two-dimensional Navier Stokes inverse solver
for compressor and turbine blade design.
Proceeding of the IMECH E part A, Journal of
Power and Energy 211, 299-307.
Henne, P. A. (1980). An inverse transonic wing
design method. AIAA Paper 80-0330.
Volpe, G. (1989). Inverse design of airfoil contours:
constraints, numerical method applications. See
AGARD, Paper 4.
Barger, R. L. and C. W. Brooks (1974). A streamline
curvature method for design of supercritical and
subcritical airfoils. NASA TN D-7770.
Garabedian, P. and G. McFadden (1982). Design of
supercritical swept wings. AIAA Journal 30(3),
444–446.
Malone, J., J. Vadyak and L. N. Sankar (1986).
Inverse aerodynamic design method for aircraft
components. Journal of Aircraft 24(1), 8–9.
Malone, J., J. Vadyak and L. N. Sankar (1986). A
technique for the inverse aerodynamic design of
nacelles and wing configurations. AIAA Paper
85–4096.
Campbell, R. L. and L. A. Smith (1987). A hybrid
algorithm for transonic airfoil and wing design.
AIAA Paper 87–2552.
Bell, R. A. and R. D. Cedar (1991, October). An
inverse method for the aerodynamic design of
three-dimensional aircraft engine nacelles. In
G.S. Dulikravich (Ed.), Proceedings of the Third
International Conference on Inverse Design
Concepts and Optimization in Engineering
Sciences ICIDES-III, Washington, D.C., USA
405–417.
Malone, J. B., J. C. Narramore and L. N. Sankar
(1989). An efficient airfoil design method using
the Navier–Stokes equations. AGARD, Paper 5.
Malone, J. B., J. C. Narramore and L. N. Sankar
(1991). Airfoil design method using the Navier–
Stokes equations. Journal of Aircraft 28(3), 216–
224.
Takanashi, S. (1985). Iterative three-dimensional
transonic wing design using integral equations.
Journal of Aircraft 22, pp. 655–660.
Hirose, N., S. Takanashi, and N. Kawai (1987).
Transonic airfoil design procedure utilizing a
Navier–Stokes analysis code. AIAA Journal
25(3), 353–359.
Dulikravich, G. S. and D. P. Baker (1999).
Aerodynamic shape inverse design using a
Fourier series method. AIAA Paper 99–0185.
Aungier, R. H. (2000). Centrifugal Compressor, A
Strategy for Aerodynamic Design and Analysis.
New York, USA, ASME Press.
Vanco, M. R. (1972). Fortran program for calculating
velocities in the meridional plane of a
turbomachine. NASA TN D-6701.
Zangeneh, M., W. N. Dawes and W. R. Hawthorne
(1988). Three-dimensional flow in radial-inflow
turbine. ASME paper No. 88-GT-103.
Nili-Ahmadabadi, M., M. Durali, A. Hajilouy and F.
Ghadak (2009). Inverse design of 2D subsonic
ducts using flexible string algorithm. Inverse
Problems in Science and Engineering 17(8),
1037-1057.
Nili-Ahmadabadi, M., A. Hajilouy, M. Durali, and F.
Ghadak (2009). Duct design in subsonic &
supersonic flow regimes with & without Shock
using flexible string algorithm. Proceedings of
M. Nili-Ahmadabadi et al. / JAFM, Vol. 7, No. 2, pp. 329-344, 2014.
344
ASME Turbo Expo 2009, Florida, USA,
GT2009-59744.
Nili-Ahmadabadi, M., A. Hajilouy, M. Durali, and F.
Ghadak (2008, August). Inverse design of 2D
ducts for incompressible viscous flow using
flexible string algorithm. Proceedings of the 12th
Asian Congress of Fluid Mechanics, Daejeon,
Korea.
Menter, F. R., M. Kuntz and R. Langtry (2003).
Ten years of industrial experience with
the SST turbulence model. In K. Hanjalic,
Y. Nagano and M. Tummers, (Ed.), Turbulence,
Heat and Mass Transfer 4, 625-632.
Ferziger, J. H. and M. Peric (1996). Computational
Methods for Fluid Dynamics. Berlin, Germany,
Springer.
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